$12 ≠ $15

[6chars]

1. wrong

Let a=12 and b=15. Define x as the difference between them:
x = b - a

Multiply both sides of the equation by (b-a):
b – a) = (b – a)(b – a)
or
bx – ax = b^2 – 2ab + a^2

Adding –bx+ab-a^2 to both sides and simplifying gives:
bx – ax – bx + ab – a^2 = b^2 – 2ab + a^2 – bx + ab – a^2

this can be rewritten as:
bx – bx – ax + ab – a^2 = –bx + b^2 – 2ab + ab + a^2 – a^2

which simplifies to:
–ax + ab – a^2 = –bx + b^2 – ab

Both sides of this equation have a common factor:
a(–x + b – a) = b(–x + b – a)

Divide both sides by (-x+b-a):

and we get

a = b, and thus 12 = 15.